Klt singularities of horospherical pairs

Pasquier, Boris

Annales de l'Institut Fourier, Tome 66 (2016) no. 5, pp. 2157-2167.

Soient $X$ une $G$ variété horosphérique et $D$ un $\mathbb{Q}$-diviseur de $X$ stable sous l’action d’un sous-groupe de Borel $B$ de $G$ et tel que $D+K_X$ est $\mathbb{Q}$-Cartier. Nous démontrons, en utilisant les résolutions de Bott-Samelson, que la paire $(X,D)$ est klt si et seulement si $\lfloor D\rfloor =0$.

Let $X$ be a horospherical $G$-variety and let $D$ be an effective $\mathbb{Q}$-divisor of $X$ that is stable under the action of a Borel subgroup $B$ of $G$ and such that $D+K_X$ is $\mathbb{Q}$-Cartier. We prove, using Bott–Samelson resolutions, that the pair $(X,D)$ is klt if and only if $\lfloor D\rfloor =0$.

Classification : 14E30, 14M15, 14M27
Keywords: klt pairs, flag varieties, horospherical varieties, Bott–Samelson resolutions
Mot clés : Paires klt, variétiés de drapeaux, variétés horosphériques, résolutions de Bott-Samelson

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